I think the hole helps the burger cook more evenly. I use the same trick when making Falafel (fried chick pea patties). This allows the center to cook all the way through. I believe the doughnut people put the hole for that reason as well.

Donut hole burgers keep the burger from shrinking into a ball like you see so many people do ending up with something that more closely resembles a meatballl than a burger (ick). Rather than poke holes in mine to avoid this, I simply make mine concave in the middle so they cook up evenly. I use a hamburger form from Tupperware to start with. I weigh out the meat and then put them in the form and press them into shape. This way I avoid overhandling the meat and my patties are uniform. After I remove the pattie from the form, I use my palm to press in the middle to make the patties concave. When you cook them, the shrinkage makes up for the concaveness resulting in a burger the same relative thickness and thus, doneness.

BBcue-Z, and Airfoils..I had never heard of holes in burgers until I read about them on another post, and reading about them. Actually I thought it was kind of a novelty thing. One day, my wife and I were at a Costco (we belong to Sam's Club), and I saw pre-formed burgers with the hole in them. I figured that I must have really been in the dark on this one. Everything you guys said makes a lot of sense.

I tried posting to this topic yesterday and my computer suffered a "Windows Protection Error". Pete, I recommend using the hole in larger burgers, especially "filled" ones. You can see pictures of burgers with holes on my link and see that they did not shrink up into a meatball. Others that I've done before these have. Give it a try and you'll agree!

White Castle has holes in their patties too. It's not a central hole but a flat pattie resembling pegboard. I believe they even use a steam cooking proccess.
White Castles and Krystals may only be hamburgers in the acedemic sense. Theyre beef patties on buns (sort of). I call em "beef cookies" rather than hamburgers.